Isomorphous phase transitions

Another example of this kind of transition is shown in table 11.1, taken from the work of Smith and Kmetko [601]. It is a quasiperiodic table of all the transition elements and lanthanides in the periodic table, arranged in order of mean localised radius in the vertical direction, and adjusted horizontally so that filled and empty d and / subshells coincide. What Smith and Kmetko discovered is that a broad diagonal sweep across this table separates metals with localised electron properties (magnets) from those with itinerant electron properties (conductors). This boundary (shown as a shaded curve in the figure) is the locus of the Mott transition. Metals lying along this curve are sensitive to pressure effects (Ce has an isomorphic phase transition from the a to the 7 phase at about 1 kbar, U becomes... 

A well-known example of critical phenomena encountered in solid state physics is the pressure-sensitive isomorphic phase transition in the amorphous solid SmS [621]. A similar effect is the a-y transition on solid Ce. In both cases, the structure of the solid does not change, but there is... 

Cey xThx- This system crystallizes in the fee structure and undergoes an isomorphic phase transition around Tg = 150 K (Shapiro et al. 1977). The transition involves a reduction in unit cell volume of 16% and is of first order for x < 0.26 and of second order otherwise. For T > one observes Cmie-type susceptibility. At the magnitude of x drops by 60% and x then remains essentially independent of temperature (Lawrence et al. 1975). 

The deviations from Vegard s law, as shown in the figure, are due to the change of the samarium valence, Welber, Jayaraman [5]. A similar curve of the lattice constants for samples obtained by a dynamical high pressure method is given by Batsanov et al. [1]. No variation of a (=6.20 A) is observed on films between x = 0 and 0.15 because of the inaccuracy of the measurements by Dumas, Schlenker [3]. The shift of the line in the X-ray spectrum of Smi xNdxSe mixed crystals remains close to zero (i.e., no isomorphous phase transition occurs), for a figure, see the paper, Sumbaev [6]. 

This transition produces an isomorphous phase and the resulting y-alumina has the same morphology and texture as its boehmite precursor. With increasing temperature and time the mean pore diameter increases gradually and other phases appear (S-, 6-alumina). Due to the broad XRD lines, the distinction between y- and S-alumina cannot be made 6-alumina occurs at about 900°C while the conversion to the chemically very stable a-alumina phase takes place at T> 1000°C. Some typical results for alumina membranes synthesized without binders are given in Table 2.4. When PVA was used as a binder, thermogravimetric analysis showed that, provided the appropriate binder type was used, the binder could be effectively removed at T > 400°C. The ash residue is of the order of 0.01 wt.%. Mean pore size and... 

Substitution of Ba with Sr slightly increases the value of the critical temperature (T 40K for x 0.15) (23). Structural analyses of (Lax 8BSr01B)Cu04 have shown that this compound has a phase transition at -200K and that its structure is isomorphic with that of (Lax 8BBa01B)Cu04 at room temperature as well as at low temperature (24)-(26). The lattice parameters for this composition are given in... 

There is agreement over the gross structural features of these linear chain chromium(II) complexes (and the isomorphous copper(II) analogues), but different models have been used for structural refinement. Phase transitions associated with the Jahn-Teller distortion (or to fi to y as the temperature is lowered) complicate the structural studies. 

The electric conductivity was also measured for complexes of taper-shaped mesogens with oligo(ethylene oxide) central groups. The DC conductivity is in a range of 10 9 to 10 6 S cm-1 and shows a step-like increase at the crystal-columnar phase transition [86]. It was also shown that taper-shaped molecules adjacent to different endo-receptors such as crown ethers or oligo(ethylene oxide) chains were miscible with a poly(methacrylate) matrix and formed isomorphic phases [87]. Applications as columnar reaction media for polymerizations were foreseen. Comprehensive summaries of Percec s taper-shaped molecules can be found in the literature [88, 89]. 

Figure 14 Precipitation of [(r 5-C5H5)2Fe]+ as its [AsFg]- salt generates two concomitant crystals a trigonal phase (Fe-T) and a monoclinic phase (Fe-M), which can be separated out by heteromolecular seeding with isomorphous crystals of trigonal [(r 5-C5Fl5)2Co][AsF6] and of monoclinic [(r 5C5Fl5)2Fe][PF6]. The crystals are sufficiently robust to undergo a full cycle of four phase transitions directly on the diffractometer, Fe-T — Fe-M — Fe-C — Fe-M - Fe-T.

Siegel and Northrop provide X-ray powder evidence to show that the phase transition, observed for each of the solid hexafluorides of the second and third transition series, involves a low temperature orthorhombic form, evidently isomorphous with orthorhombic OsOF and a cubic high temperature from isomorphous with cubic OsOF. The equivalence of die Bravais lattices and the close similarity of the unit cell dimensions implies close structural similarity of the low temperature phases. The higher temperature, cubic phases, are on the X-ray evidence, body-centred cubic. 

It is clear that in the case of MFI, the zeolite pore entrances should not be considered as rigid apertures. Instead, zeolite framework topologies can show flexibility. While the O-Si-0 angle in the tetrahedral unit is rigid (109 + 1 °), the Si-O-Si angle between the units can vary between 145 and 180°. Based on isomorphous substitution of Si by other T-atoms in the framework [18], framework defects [19], cation positions, changes in the water content [16], external forces on the crystalline material [20] and upon adsorption of guest molecules [21] phase transitions can occur that have a dramatic influence in particular cases on the framework atom positions. 

The method proposed by Parrinello and Rahman is of special interest in studies of crystalline solids and zeolites in particular. The method allows a variation of both volume and shape of simulation box and therefore is suitable for studying phase transitions induced by sorption of molecules, isomorphic substitution, or change of temperature. In this method, the Lagrangian of a system with kinetic energy T and potential energy U... 

Figure 32 Precipitation of [Fe( -C5H5)2] as its [AsFe] sait generates two concomitant crystais a trigonai phase (Fe-T) and a monociinic phase (Fe-M), which can be separated out by heteromoiecuiar seeding with isomorphous crystais of trigonai [Co( 7 -C5H5)2][AsFe] and of monociinic [Fe(rj C5H5)2][PFe]. The crystais are sufficientiy robust to undergo a fuii cycie of four phase transitions directiy on the diffractometer, Fe-T Fe-M —> Fe-C Fe-M Fe-T.

West [23] reported that TIN3 is isomorphous with KN3 with the unit-cell dimensions a = 6.21 and c = 7.37 A. Recently Muller [19] investigated the structure of TIN3 by X-ray diffraction and obtained N-N = 1.16(24) and Tl-N = 3.04(3) A. A recent neutron-diffraction study [7] revealed that the Nj ions undergo very large librational motion, not only at room temperature but also at lower temperature (260°K). The N-N bonds, corrected for librations, were 1.181(4) A for the room temperature and 1.184(1) A for the 260°K structure. Recently Mauer et al. [24] have studied the phase transitions of TIN3 by X-ray... 

Exact solutions, as obtained for uni-versahty classes of 2D systems such as the 2D-Ising (isomorphic to the lattice gas) or 3-state Potts model, are important but do not contain any qualitative insight into the nature of the respective continuous phase transitions. Such an insight is given by the (1) renormalization group [61], which explains how the quaU-tative features of the cooperative behavior arise, (2) series expansion techniques [60], (3) MC simulations [33, 38, 62] and in situ structure-sensitive experimental studies with the spatial resolution of individual atoms and/or molecules. 

In this work, we present results of dielectric measurements of two diacetylenes pTS (R = CH2-0-S02-< )-CH3) and pFBS (R = CH2-0 S02-< F). At room temperature, and down to ca. 200 K, both crystals are isomorphous (monoclinic P2i/c, Z = 2), with almost identical crystallographic paclangs [7-9]. The monomer of pTS exhibits two phase transitions (at ca. 200 K and ca. 160 K), the phase between them being incommensurate [10]. The low-T phase remains P2j/c, with four molecules per unit cell [8]. Poly-pTS displays only one phase transition, at ca. 190 K, directly to the low-T phase, which is isomorphous with that of monomer [11]. On the other hand, spectroscopic investigations of polymerized pFBS [12] did not show any evidence of a phase transition, from troom temperature down to 4 K. 

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